Scattering of Metastable Mercury Atoms BY T. A. DAVIDSON, M. A. D. FLUENDY AND K. P. LAWLEY Dept. of Chemistry, University of Edinburgh, Edinburgh EH9 355 Received 10th January, 1973 Differential elastic cross sections for the scattering of the metastable 6 3Pz state of mercury from sodium, potassium and rubidium have been measured at thermal energies. Interference structure is resolved in all cases, suggesting that the atoms interact by a single effective potential in the attractive region probed at these energies. No attenuation of the interference structure is observed so that quenching of the metastable state is not an important process along trajectories sampling only the attractive part of the potential. Collisions between ground state Hg atoms (IS,) and alkali metal atoms (”&) at thermal energies are necessarily elastic and occur under the influence of a single potential.Scattering measurements on these systems have been made by several groups 1-7 and recently Buck and Pauly ’* have reported accurate differential cross section measurements and their inversion to yield potentials. This inversion may be in some degree ambiguous as shown by Boyle lo ; nevertheless the potential between the alkali metals and ground state mercury is now comparatively well established. The corresponding interaction between alkali atoms and the excited states of Hg l 2 is much less well understood. The lowest of such states are the 63P0, 63P1 and 63P, at, respectively, 4.64,4.89 and 5.43 eV above ground. The 63P0 and 63P2 states are metastable with a lifetime 11* l2 - s, comparable to the flight time in the crossed beam apparatus used for the present experiments.The 3P1 state decays after - s. The thermal energy collision of these atoms with other species is now complicated not only by the possibility of electronic energy transfer but also by the fact that a manifold of potentials arises from the separated atoms due to the possible spin pairings (if the partner is not a singlet atom) and mJ states of the Hg atom. TABLE 1.-AE FOR PROCESSES INVOLVING Hg (3P2) AND ALKALI METALS process ionisation of M Na - 0.31 - K Rb 1.11 - 1.27 excitation transfer to 1st excited state of M - 3.33 - 3.82 - 3.87 The photochemistry l3 of these states and in particular of the 3P1 atoms is of great importance and has been widely studied. However, the understanding of the funda- mental processes of electronic energy transfer and their relation to curve crossing must begin with simple systems where a knowledge of the adiabatic potential curves can be obtained.The alkali metal+Hg* system is a useful case for this purpose since both theoretical studies and the unravelling of potential energy curves through magnetic state selection offer the hope of a complete picture. The various processes that can occur are : (a) elastic scattering, (b) intermultiplet transitions AJ, which will be followed by quenching if the 3P1 state is formed, (c) 158T . A . DAVIDSON, M . A . D. FLUENDY AND K . P . LAWLEY 159 Am, transitions within a given J state, (d) ionisation, (e) transfer of electronic excitation to the alkali metal.For the 63P2 state, all these channels are open for the series Na to Cs, though with fairly considerable exoergicities except for cases (a) and (c) ; exoergicity values are given in table 1. In this paper we describe the results of differential cross section measurements on the process (a), elastic scattering accompanied by (c), rn J transitions, i.e., for scattering without change in J value. EXPERIMENTAL The apparatus is shown schematically in fig. I . The two beam sources rotate on a turn- table in front of the fixed detector which is located in a differentially pumped chamber.14 The excited mercury beam is produced by bombarding a ground state Hg beam effusing from a glass capillary array with electrons of controlled energy.The electrons were collimated by a magnetic field and, with an excitation voltage of 10 eV, an electron current - 10 mA excited roughly 1 in lo5 of the Hg atoms resulting in a metastable flux of 101o-lO'l atoms steradian-l s-l. Higher electron energies mainly resulted in increased production of photons as shown by time of flight experiments using a pulsed excitation voltage. After re-collimation (the electron bombardment can produce deflections -2" in the Hg* beam), the metastable atoms crossed a modulated target beam of alkali metal atoms. The scattered atoms entered a UHV chamber (- Torr) via a narrow channel to strike a clean potassium surface plated in situ. Electrons ejected from this surface were focused into a Mullard channel electron multiplier and counted on dual scalers gated in delayed synchronism with the target beam modulation.The maximum counting rate observed was -lo5 Hz while the background count rate for the detector alone (valved off from the main chamber) was 1-0.1 Hz; more typically, when measurements were in progress, the background was 2-3 Hz. Once prepared, the K surface was stable in performance for periods of several months. All the experimental data were recorded on paper tape and processed off line by computer.14 HCJ' OVEN XBEAM WEN ts.p. 1 FIG. 1 .-Apparatus schematic showing electron gun for metastable Hg production and the Auger detector.I 60 SCATTERING OF METASTABLE MERCURY ATOMS The excitation function observed with this equipment is shown in fig. 2 as a plot of main beam signal (normalised by the excitation current) versus excitation voltage.The first maximum with a threshold at -6.0 eV arises from the 6 3Po,l,a states, the other maximum with a threshold at 10 eV observed on a tungsten surface results from photons plus possibly some long lived 303 Hg atoms.lS In the results to be described, 10 eV electrons were used so that only the 63P0,1,2 states need be considered. Of these three possibilities, time of flight experiments showed the photon contribution (from decay of 3P1 Hg) to be only - 10 % of the total signal. Since the scattering cross section for 2537 A photons with alkali metals is very much smaller than for atom-atom collisions, these photons will not be modulated by the cross beam and hence not registered as scattered signal.Calculations l6 for the 3P2 and 3P0 states suggest that the ratio of their cross sections for formation by electron bombardment is roughtly 5 : 1 (i.e., the simple statistical ratio). Their lifetimes are probably similar and since the 3P2 would be more efficiently detected by the K surface, the observed scattering is tentatively attributed solely to this state. Magnetic deflection analysis of the beam to confirm this is in progress. 2 4 6 .8 113 12 14 16 exciter volt age/V FIG. 2.-Apparent excitation function observed for Auger ejection from K and W surfaces as a function of exciter voltage in the source. Because the 3P2 Hg atom flux decays appreciably during transit from scattering centre to detector, the Hg* velocity distribution is considerably distorted from the initial v 2 Maxwellian one out of the exciter.The appropriate velocity distribution a distance L from the source is : where v g is the most probable velocity at source and z is the lifetime. downstream, the most probable velocity v z is given by the appropriate root of the cubic At a distance L From the dimensions of the apparatus (L = 61 cm), the most probable velocity of the Hg* is - 38 % greater than that for a stable species at the same temperature. The relative velocity distribution is not affected so much, the full width at half height being reduced by 10 %. The most probable relative velocity also changes slightly with angle of scattering. Finally, the relative masses and velocities are such that at a given laboratory angle of observation (0) there are two centre of mass angles (x) contributing, leading to fast and slow scatteredT.A . DAVIDSON, M. A . D. FLUENDY A N D K . P . LAWLEY 161 components. However, partly because of the ratio of Jacobians but also because of sub- stantially greater decay, the slow component is <10 % of the fast component and may be neglected. RESULTS AND DISCUSSION Laboratory distribution for HgZk elastically scattered from the alkali metals Na, K and Rb are shown in fig. 3,5 and 7. The corresponding centre of mass angles are also shown on the axes. The results for Rb are rather limited in precision pending further observations. Fig. 4 and 6 show the result of deconvoluting the curves shown in fig. 0' 25 44 angle 75 FIG. 3.-Laboratory differential cross section for Hg 63P2 scattering from sodium.The angles shown below the axis are in the centre of mass system. Velocity 895.0 m s"'. 1 t m t- 0 u M (d X x 1 Y CI Y .d c) $ .- <!I 4 n 0 25 44 75 angle FIG. 4.-Laboratory differential cross section for Hg 63P2 +Na deconvoluted using the main beam profile, data of fig. 3. 55-F162 SCATTERING OF METASTABLE MERCURY ATOMS 3 and 5 using the observed main beam profile as the filter function. The deconvoluted results are rather noisy, but structure partially resolved before deconvolution can now be clearly seen. The laboratory angles are shown above the axis. angle FIG. 5.-Laboratory differential cross section Hg 6 3 P ~ scattering from K. The angles shown below the axis are in the centre of mass system. Velocity 660.0 m s-l. 0 2 0 63 angle FIG.6.-Deconvoluted results for Hg 63Pz+K, same data as fig. 5. The most striking qualitative feature of these results is the presence of strong undulations in the differential cross sections which cover the whole angular range of observation (out to 85" in the centre of mats in some cases) with undiminished ampli- tude. This points to two quite separate conclusions. Firstly, we are seeing the operation of either a single potential or a group of potentials that are very similar inT . A . DAVIDSON, M . A . D . FLUENDY AND K . P . LAWLEY 163 the parts of them covered by the observations. For, if several rather different potentials with similar weights were operating, the net interference structure would be much weakened by superposition of the separate patterns. Furthermore, the presence of strong interference structure means that at least two branches of the deflection function are present.Thus, quenching cannot be removing the inner branch of the deflection function or, if several similar potentials are operating, only one or two at most can be affected in this way otherwise the amplitude of the interference structure would be diminished. FIG. 7.-Laboratory differential cross section for Hg 63P2 scattering from Rb. The angles shown below the axis are in the centre of mass system, Velocity 470.0 m s-l. FIG. &--A family of deflection functions arising from a group of potentials having similar values of u and C, but different values of E. Also shown are the I values of some interfering branches.1 64 SCATTERING OF METASTABLE MERCURY ATOMS Turning to the details of the scattering structure, there is a regular pattern in which two periods may be seen, a high frequency one with an average period of -5.8" (Na) and 3.7" (K) and a lower frequency one of smaller amplitude with a period of 24" and 13" respectively in Na and K. This rather simple structure is similar to that expected from a single potential at collision energies leading to orbiting or a rainbow well beyond the angular observation range.Referring to fig. 8, analysis of the angular periods in the interference structure can be made using the semi-classical relation Ax = 2n/(Z, -Z2) where ZI and Z2 are the orbital momenta values for two interfering branches on the attractive side. The high frequency oscillations would then corres- pond to interference between two attractive branches with deflection x and spaced 2-3 A apart.The low amplitude longer period oscillations similarly arise from regions of the deflection function centred at 2n-x and x, spaced -0.8 A apart, (see fig. 8). A detailed potential fit to this data has not yet been achieved but at least a qualitatively similar cross section can be obtained using the Buck and Pauly potential for the ground state atoms, suggesting that the effective potential of Hg*/M is similar to this. Five molecular states evolve from the atomic pair Hg(3P2)+M(2St) and so the question arises as to why they should all appear so similar. At large separations Hund's case (c) holds (assuming fixed nuclei) and the manifold of states may be classified by their value of Q(= m,(Hg)+m,(M)).In the limit of small separations (Hund's case (a)) the good quantum numbers are A and S. Depending on the order of the molecular states, the following tentative correlations may be made ; molecular mJ ms Q state It is clear that neither the deep lying 2C+ nor the largely repulsive 2Zz correlate with the 3P2 state. Calculations of the interatomic potential in the m,, m, coupling scheme have been made using the limited Hartree-Fock-Slater 2-electron orbitals already calculated for the 3P2 state of Hg.17 These were combined with HFS valence orbital of the alkali metal to form a linear combination of Slater determinants that preserved J and mJ as good quantum numbers. An approximate Hamiltonian using the core potentials (with exchange) of the unperturbed atoms together with the specific electron-electron repulsion terms among the three valence electrons was then used in a first order computation of the energy of each of the five states listed above.Relatively shallow wells ranging from 8 x erg to 13 x erg were found, all much less than the spin-orbit splitting in mercury. The positions of the potential minima were roughly constant at 4 A. The calculated potentials thus bracket the ground state well depth but have rather smaller values of Q. So far, then, we have a picture of five rather similar potentials originating with the 3P2 states, partly as a result of the restrictions of the correlation diagram itself. Turning to the dynamics of the collision, the forces operating depend upon whether mJ in a space fixed system or in a rotating system is a good quantum number.Thus for collisions of large impact parameter the coupling of electronic motion to the inter- atomic motion is weak and the phase shifts depend only slightly on mJ. That is, the adiabatic phase shifts (those calculated assuming mJ a good quantum number) are scrambled. As the impact parameter decreases strong coupling ensues, at first nearT . A . DAVIDSON, M. A . D . FLUENDY AND K . P. LAWLEY 165 the turning point. Finally, for collisions of small impact parameter, mJ in a rotating frame is a good quantum number and the phase shift functions are well separated. The impact parameter at which coupling becomes important is determined by the splitting of the adiabatic potentials.of the 3Pz state on mJ is less than 10 % of the mean value and this presumably means a similarly small range of c6 values. Taking the range of C6 values to be given effect- ively by The dependence of the polarisability A c 6 = 4 A d (3) where A& is the range of well depths quoted above and applying l9 to determine the critical impact parameter for coupling, b,, values N 6 A are obtained with a relative velocity U- 6.6 x 10’ m s-l. At small angles of scattering, the lack of coupling between the Hg* mJ state and the passing atom results in a scrambling of the manifold of interatomic potentials to give one effective potential curve. As b decreases, coupling ensues but the potentials, all belonging to quartet states, remain inherently similar and the interference structure from them coincides. The observa- tion of a weak structure of longer periodicity in o(0) shows that the deflection functions associated with the various adiabatic potentials can not diverge appreciably until near the minimum where the resulting interference structure from each state would be lost (see fig.8) in the averaging over mJ. The observation of quantum structure also sets an upper limit on the size of the quenching cross section since both branches of the deflection function must be present for this structure to be seen. In the absence of a detailed potential fit to the experi- mental data, it is not possible to give a precise value to this limit, but quenching is clearly not an important process for collisions with impact parameters >o and the total quenching cross section can hardly exceed gas kinetic values.No other data on the absolute magnitude of the quenching cross section for Hg 6 3Pz have been reported, though Martin 2o has measured relative total cross sections for the intermultiplet process (d) with a wide range of gases ; preliminary results 21 for excitation of the alkali metals are not incompatible with a cross section of gas kinetic magnitude. We thus adopt the following tentative picture. The authors thank the Science Research Council and N.A.T.O. for financial support and T. A. D. the Carnegie Trust for a scholarship. F. A. Morse and R. B. Bernstein, J. Chem. Phys., 1962,37,2019. F. A. Morse, R. B. Bernstein and H. U. Hostettler, J. Chem Phys, 1962, 36, 1947. H. U. Hostettler and R. 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